Find a quadratic polynomial,each with the given numbers as the sum and product of its zeroes respectively: $\sqrt{2}, \frac{1}{3}$.

(D) Let the quadratic polynomial be $p(x) = ax^2 + bx + c$,and its zeroes be $\alpha$ and $\beta$.
The sum of the zeroes is given by $\alpha + \beta = \sqrt{2} = -\frac{b}{a}$.
The product of the zeroes is given by $\alpha \beta = \frac{1}{3} = \frac{c}{a}$.
To express these with a common denominator $a$,we write $\alpha + \beta = \frac{3\sqrt{2}}{3} = -\frac{b}{a}$.
Comparing the coefficients,we get $a = 3$,$b = -3\sqrt{2}$,and $c = 1$.
Substituting these values into the general form $ax^2 + bx + c$,we get the quadratic polynomial $3x^2 - 3\sqrt{2}x + 1$.